Hairs on the cosmological horizon

TL;DR

This paper explores the existence of 'hairs' on the cosmological horizon, demonstrating conditions under which scalar hair can or cannot exist, and proving no-hair theorems for certain spacetime geometries.

Contribution

It extends the no-hair theorem to cosmological horizons, proving the absence of scalar hair in anti-de Sitter and de Sitter black holes under specific conditions.

Findings

No scalar hair for anti-de Sitter black holes.

No scalar hair for de Sitter black holes with convex potential.

Matter fields in Q-stars and boson stars do not reach the cosmological horizon.

Abstract

We investigate the possibility of having hairs on the cosmological horizon. The cosmological horizon shares similar properties of black hole horizons in the aspect of having hairs on the horizons. For those theories admitting haired black hole solutions, the nontrivial matter fields may reach and extend beyond the cosmological horizon. For Q-stars and boson stars, the matter fields cannot reach the cosmological horizon. The no short hair conjecture keeps valid, despite the asymptotic behavior (de Sitter or anti-de Sitter) of black hole solutions. We prove the no scalar hair theorem for anti-de Sitter black holes. Using the Bekenstein's identity method, we also prove the no scalar hair theorem for the de Sitter space and de Sitter black holes if the scalar potential is convex.